Inventory Modeling for Imperfect Production Process with Inspection Errors, Sales Return, and Imperfect Rework Process

In real life, due to certain machine problems, process deterioration and many other factors, production processes deliver imperfect quality items. So, the effect of these defectives cannot be ignored in terms of ensuring good customer service. In order to sustain today’s cut-throat competition, rework process of defective items becomes a rescue to compensate for the imperfections present in the production system. The present model attempts to explore the traditional imperfect environment with a more practical approach by incorporating the concept of inspection errors, along with an imperfect rework process. By considering human errors as unavoidable, Type-I and Type-II errors are also incorporated in the study. To prioritize on the customer satisfaction level, Sales returns are given full price refunds. An analytical method is employed to maximize the expected total profit per unit time to study the combined effect of aforementioned factors on the optimal production quantity. A numerical example along with a comprehensive sensitivity analysis has been presented to demonstrate the applicability of the model and also to observe the effects of key parameters on the optimal production policy respectively. The pertinence of the model can be found in most manufacturing industries like textile, electronics, furniture, footwear, crockery etc.